One of the most attractive phenomena in condensed matter physics is the
existence and behavior of edge states, whose wave function is localized at
the system's edge, of two-dimensional (2D) systems. These states are
different from the bulk states in properties and play important roles in
transport, e.g. quantum Hall effect (QHE) and the quantum spin Hall effect
(QSHE) [1]}, [2]}, [3]}, [4]}.On the other hand, the existence and
properties of zero-energy edge states near the Fermi level (flat bands) are
usually connected with the non-trivial topological phases of the bulk system
by the bulk-edge correspondence [5]}, [6]}, [7]}, [8]}, [9]}, which can
be distinguished by the specific symmetry of the system and topological
invariants such as the winding number [8]}, [9]}, [12]}, [13]}.
